Integrals of periodic motion for classical equations of relativistic string with masses at ends

Boundary equations for the relativistic string with masses at ends are formulated in terms of geometrical invariants of world trajectories of masses at the string ends. In the three-dimensional Minkowski space $E^1_2$, there are two invariants of that sort, the curvature $K$ and torsion $\kappa$. For these equations of motion with periodic $\kappa_i(\tau+n l)=\kappa(\tau)$, constants of motion are obtained.